On the maximum of random assignment process

TL;DR

This paper analyzes the expected maximum value in a random assignment process based on a square matrix with independent entries, expressing the result through the matrix's distribution quantile function.

Contribution

It provides a novel characterization of the maximum's expectation in random assignment processes using distribution quantiles under mild assumptions.

Findings

Expectation of maximum is expressed via quantile function.

Results apply to matrices with independent entries.

Provides insights into the behavior of random assignment maxima.

Abstract

We describe the behavior of the expectation of the maximum for a random assignment process built upon a square matrix with independent entries. Under mild assumptions on the underlying distribution, the answer is expressed in terms of its quantile function.